Transcript IIR Ultra-Wideband Pulse Shaper Design

IIR Ultra-Wideband
Pulse Shaper Design
Chun-yang Chen and P.P. Vaidyananthan
California Institute of Technology
DSP Group, EE, Caltech, Pasadena CA
The UWB communications


In 2002, the Federal
Communication
Community (FCC)
approved a spectral
mask for operation of
UWB devices.
It allows UWB
devices operate on
3.1GHz ~ 10.6GHz
under -41.3dBm.
DSP Group, EE, Caltech, Pasadena CA
Impulse radio system for UWB


Impulse radio system transmits very short pulses
p(t) without RF carriers.
The radiated power spectrum of impulse radio
system can be expressed by
2
S ( f )  H eq ( f ) S m ( f ) P( f )
Transfer function
from modulated
pulse train to
radiated signal
Depends on the
modulation method
DSP Group, EE, Caltech, Pasadena CA
2
 M( f )
Fourier
transform of
the pulse
Example of Gaussian monocycle pulse

For example, if we use the Gaussian
monocycle pulse (derivative of a Gaussian
pulse), then
t
2( )2
p (t )  2 e
t
g
e
g
Assume Heq ( f )  Sm ( f )  1
Then the radiated power spectrum is
 f  g
S ( f )  f exp(
)
2
2
2
DSP Group, EE, Caltech, Pasadena CA
2
2
Example of Gaussian monocycle pulse (2)
The power spectrum for using Gaussian monocycle
pulse

-40
 f  g
S ( f )  f exp(
)
2
2
-50
Power(dBm)
-60
2
-70
-80
Mask
g=10ns
-90
g=50ns
-100
g=100ns
0
2
4
6
8
Frequency(GHz)
10
12
DSP Group, EE, Caltech, Pasadena CA
The transmitting
power is very
small.
2
2
The optimization problem

To utilize the bandwidth, the optimal pulse
should be designed so that the transmitting
power is maximized.
Fmax
max
p (t )

2
2
H eq ( f ) S m ( f ) P( f ) df
Fmin
2
subject t o H eq ( f ) S m ( f ) P( f )  M ( f )

2
The ideal solution to this problem is the pulse
2
2
such that
H ( f ) S ( f ) P( f )  M ( f )
eq
m
DSP Group, EE, Caltech, Pasadena CA
Mask filling efficiency

The mask filling efficiency [Lewis et al. 2004] is
defined as


Fmax
Fmin
2
H eq ( f ) S m ( f ) P( f ) df

Fmax
Fmin

2
M ( f )df
The ideal solution
2
H eq ( f ) S m ( f ) P( f )  M ( f )
yields 100% of efficiency.
DSP Group, EE, Caltech, Pasadena CA
2
Pulse shaper

However, we cannot generate pulse with
arbitrary P ( f ) with analog circuits.

We can generate the pulse by shaping
the available waveforms by
M
p(t )   bn g (t  nT )
n 0
This waveform can be
directly generated by analog
circuit.
DSP Group, EE, Caltech, Pasadena CA
The scheme of FIR pulse
shaper
M
p(t )   bn g (t  nT )
n 0

D denotes the analog delay.
DSP Group, EE, Caltech, Pasadena CA
Power spectrum of the
radiated signal
M
p(t )   bn g (t  nT )
n 0

The Fourier transform of the pulse is
M
P( f )   bn e
i
2n
f
T
G( f ).
n 0

The power spectrum of the radiated
signal is
S( f ) 
M
b e
n 0
n
2n 2
i
f
T
2
2
G ( f ) H eq ( f ) S m ( f ).
DSP Group, EE, Caltech, Pasadena CA
Design of the pulse shaper

To approximate the ideal solution, we choose
the shaper {bn } so that
S( f ) 
M
b e
n 0


n
2n 2
i
f
T
2
G ( f ) H eq ( f ) S m ( f )  M ( f ).
2
It reduces to an FIR filter design problem.
Standard technique such as the ParksMcClellan algorithm can be used to design
such a filter [Luo et all. 2003].
DSP Group, EE, Caltech, Pasadena CA
Results of using the pulse
shaper
Gaussian
monocycle pulse
shaped by the
minimax FIR filter
-40
-45
Power (dBm)
-50
-55
Gaussian
monocycle
pulse
-60
-65
-70
M
p(t )   bn g (t  nT )
-75
-80

0
2
4
8
6
Frequency (GHz)
10
12
The multipliers of the shaper is 17.
DSP Group, EE, Caltech, Pasadena CA
n 0
IIR pulse shaper

With the same complexity, IIR filters has
better frequency response than FIR filters.

We can generate the pulse by summing
the delay version of the elementary
waveforms and the feedback
M
N
n 0
n 1
p(t )   bn g (t  nT )   an p(t  nT )
DSP Group, EE, Caltech, Pasadena CA
The scheme of IIR pulse
shaper
M
N
n 0
n 1
p(t )   bn g (t  nT )   an p(t  nT )

D denotes the analog delay.
DSP Group, EE, Caltech, Pasadena CA
Power spectrum of the
radiated signal
M
N
n 0
n 1
p(t )   bn g (t  nT )   an p(t  nT )

The Fourier transform of the pulse is
b e
i
2n
f
T
a e
i
2n
f
T
M
P( f ) 
n 0
M
n 0

n
G ( f ).
n
The power spectrum of the radiated signal is
M
S( f ) 
b e
n 0
N
2
2n
f
T
n
a e
n 0
i
2
2n
i
f
T
2
G ( f ) H eq ( f ) S m ( f ).
n
DSP Group, EE, Caltech, Pasadena CA
Design of the IIR pulse shaper

To approximate the ideal solution, we choose the
shaper {bn }nM0 and {an }nN1 so that
M
S( f ) 
b e
i
a e
i
n 0
N
n 0


2
2n
f
T
n
2n
f
T
2
G ( f ) H eq ( f ) S m ( f )  M ( f ).
2
n
It reduces to an IIR filter design problem.
However, there is no standard technique to design
IIR filter to fit arbitrary magnitude response.
DSP Group, EE, Caltech, Pasadena CA
Design of IIR pulse shaper
using Elliptic filters
There are standard techniques to design IIR filters
to fit bandpass magnitude responses such as elliptic
IIR filters.

Gaussian monocycle pulse
shaped by an elliptic IIR
filter.
Filling efficiency: 68.29%
-40
-45
Power (dBm)
-50
-55
-60
Gaussian monocycle pulse
shaped by a minimax FIR
filter.
Filling efficiency: 74.96%
-65
-70
-75
-80
0
2
4
6
8
Frequency (GHz)
10
12

Both filters have 17 multipliers.
DSP Group, EE, Caltech, Pasadena CA
Comparison Elliptic shaper
and minimax FIR shaper
Elliptic IIR shaper has sharp
transition band but cannot
compensate the nonflatness
of the transfer functions.
Minimax FIR shaper has the
flexibility to compensate the
nonflatness. But the transition
band is wide.
Power (dBm)
-40
-45
-50
-55

0
2
4
6
8
Frequency (GHz)
10
12
We can combine these
two
ideas
to CA
get both of their benefits.
DSP Group,
EE, Caltech,
Pasadena
IIR shaper design

We divided the problem into two parts.
S ( f )  H 1 (e
2n
i
f
T
2
) H 2 (e
2n
i
f
T
2
2
) G ( f ) H eq ( f ) S m ( f )  M ( f ).
2

The first part is designing the Elliptic IIR filter H1
to fit the transition band of the mask M ( f ) .

The second part is designing the minimax FIR filter
H2 to fix the nonflatness of the transfer
2
G ( f ) H eq ( f ) S m ( f ) .
functions
DSP Group, EE, Caltech, Pasadena CA
Results
Minimax FIR
shaper: efficiency =
74.96%
Elliptic IIR shaper:
efficiency = 68.29%
Combination
method: efficiency
= 78.92%
-40

Power (dBm)
-45

-50
-55
-60
0
2
4
6
8
Frequency (GHz)
10
12
DSP Group, EE, Caltech, Pasadena CA
All shapers have 17
multipliers.
Combination method
uses
7 multipliers on
minimax FIR shaper
and
10 multipliers on
Elliptic IIR shaper.
Transient response

FIR
0.15
imp. resp.
0.1
0.05
0

-0.05
-0.1
0
2
4
6
8
10
New method
imp. resp.
0.2
0.1
0
-0.2

1.5% of the energy
-0.1
0
2
4
6
8
10
The impulse response
of the FIR shapers has
a duration of 2.4ns.
The proposed method
has only 1.5% of
energy outside this
duration.
The transient response
is small.
time(ns)
DSP Group, EE, Caltech, Pasadena CA
Conclusions




The pulse design is to generate a pulse such
that radiated power can be maximized.
The IIR based pulse shaper is introduced.
An elliptic IIR filter and a minimax FIR filter
are combined to fit the mask and the transfer
functions.
The transient response of the proposed IIR
filter is small enough to be neglected.
DSP Group, EE, Caltech, Pasadena CA
References



Terry P. Lewis, Robert A. Scholtz, “An ultrawideband signal
design with power spectral density constraints,” Proc. 38th
IEEE Asilomar Conf. on Signals, Systems, and Computers, pp.
1521-25, Nov. 2004.
X. Luo., L. Yang, and G.B. Giannakis, “Designing optimal
pulse-shapers for ultra-wideband radios, ” Proc. of IEEE Conf.
on Ultra Wideband Systems and Technologies, pp. 349-353,
Nov. 2003.
B. Parr, B. Cho, K. Wallace, and Z. Ding, “A Novel UltraWideband Pulse Design Algorithm,” IEEE Comm. Letters, pp.
219-221, 2003.
DSP Group, EE, Caltech, Pasadena CA
Thank you.
DSP Group, EE, Caltech, Pasadena CA